Apparatuses of this kind are known, inter alia, from SEC-C-8305817-2 (corresponding to EP-B1-0160069 and U.S. Pat. No. -4 634 529) and have the advantage of combining a very large filter surface with a relatively small volume. However, when it comes to achieving thickening of a fiber suspension, i.e., raising the dry solids content from typically 0.5% to typically 5%, very high capacity, i.e., a large filtrate flow through the apparatus, is required. One way of increasing the flow capacity is to increase the rotation rate. However, a high rate of rotation means that the filter sections do not have time to be emptied of filtrate before the sections reach the position where the filter cake is to be removed. The reason for this is that the filter cake that is built up has time to be too dense to pass through sufficient air to replace the filtrate flowing out. It can thus occur that the filtrate wets the filter cake remaining on the filter section, or that the filtrate together with the filter cake runs down into the collection vessel intended for the filter cake. This phenomenon is usually referred to as re-wetting or "backwash". The known apparatuses are moreover expensive to manufacture, inter alia because they require a vacuum valve and a vacuum source for establishing a sufficiently large pressure difference between the suspension and the filtrate discharge duct.